If you are the original owner of the phone and it is paid off, this is the only method you should use. It is the safest route. However, if you bought a used phone that is still under contract with another person, the carrier will likely reject your request.
Avoid this unless you are a hobbyist. For the average user, the risk of breaking the phone far outweighs the money saved. how to unlock a cell phone
Verizon is the outlier. Most Verizon phones are automatically unlocked 60 days after purchase/activation, provided the account is in good standing. Third-Party Unlocking Services If you are the original owner of the